Let us look at an example in order to appreciate the point. In the Humean camp, the best systems analysis offered by Lewis is arguably the most systematic and ambitious project in that family. Lewis's reduction takes worlds as fundamental. A world, for Lewis, consists in a spatiotemporal arrangement of local qualities, i.e., “perfectly natural properties which need nothing bigger than a point at which to be instantiated” [1]}. These points may be parts of spacetime itself or “point-sized bits of matter or aether or fields” (ibid.), or both. Even in the latter case, however, there is “a system of external relations of spatiotemporal distance between points” (ibid.). We may be substantivalists or relationalists about it, but one way or the other, spacetime forms the backbone of a Lewisian world. For Lewis, spatiotemporal relations are what unify and isolate the worlds so central to his analysis. They are the `world-making' relations, i.e., the relations in which all and only worldmates stand. Spacetime thus furnishes the backbone of Lewis's project.At this point, an important caveat ought to be stated: Lewis clearly acknowledges the potential need to generalise the world-making relations from spatiotemporal relations to what he dubs `analogically spatiotemporal' relations [2]}. These relations are characterized by four conditions. First, they are natural. Second, they are pervasive, i.e., if there is a chain of relations connecting a `first' to a `last' object, then there is also a direct relation between them. Third, they are discriminating, i.e., the relational structures uniquely identify the positions in them which the relata can occupy, such that the relata are identifiable by their positions only. Fourth, they are external, i.e., “they do not supervene on the intrinsic natures of the relata taken separately, but only on the intrinsic character of the composite of the relata” [2]}. The condition of relations qualifying as analogically spatiotemporal is strictly weaker than as spatiotemporal relations, as the latter are also analogically spatiotemporal but not vice versa. For an argument why we should not in general expect the fundamental relations in quantum gravity to be even analogically spatiotemporal, see [4]}. [5]} argues that the non-local relations sometimes obtaining between quantum-mechanical systems are neither pervasive nor discriminating and so not even analogically spatiotemporal. He thus pleads to further weaken the requirement and to take two objects as worldmates if and only if they stand in a natural external relation (see also [6]} for an earlier argument that Lewis's criterion should be relaxed to a mere demand of the externality of the worldmate relation). Arguably, the (non-local) relations quantum-mechanical systems can stand in are natural and external, and can thus function as world-making relations. We concur with Darby that the demand for analogically spatiotemporal relations ought to be weakened to the wider category of natural external relations, also in light of our analysis. But we are getting ahead of ourselves.
